Dynamical Systems With Applications Using

This volume develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. This monograph lights a new energy flow research direction for nonlinear dynamics.

The book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators.

This book provides an overview of the current state of the art in this fascinating and critically important field of pure and applied mathematics, presenting recent developments in theory, modeling, algorithms, and applications.